Structural Inference of Interacting Dynamical Systems

This thesis delves into advanced methodologies for structural inference in dynamical
systems, particularly focusing on the challenge of deducing underlying interaction
graphs from observable data. The research encapsulates six seminal papers
that collectively push the boundaries of iterative optimization, deep active learning,
reservoir computing, partial correlation coefficients, and state-space models.
At the core of the contributions of this thesis is a novel iterative structural inference
model utilizing variational autoencoders. This model systematically refines interactions,
enhancing directional accuracy and incorporating regularization for better
complex systems modeling. In addition, a deep active learning framework is
introduced. It leverages neural networks to boost inference accuracy with minimal
prior knowledge, demonstrating scalability and superior performance across large-scale systems.
Our work also includes a robust benchmarking of structural inference methods,
showcasing the efficacy of integrating reservoir computing to capture interactions
within high-dimensional data contexts. This integration proves particularly effective
in handling sparse data scenarios. Furthermore, the application of partial correlation
coefficients offers a statistical technique to pinpoint direct interactions, facilitating
scalability. The incorporation of state-space models addresses the challenges
posed by irregularly observed trajectories and incomplete observations, enhancing
the robustness of our approach.
Extensive evaluations across simulated and real-world datasets confirm the scalability, precision, and robustness of these methodologies, establishing a new benchmark in the field of structural inference.